One an ODD Number
By: Yehuda Zaks
One an ODD Number
Discovering the unity of the world through numbers
One of the basic tenets of Judaism is the belief in Hashem (G-d) as both the sole
source and ongoing sustainer of the world.1 This belief implies an innate unity
of all objects and beings in the world, even though they appear to be extremely
diverse. In addition, one of Man’s key roles in the world is to discover this
hidden unity and thereby reveal and understand G-d’s presence in the world.
The aim of this article is to illustrate that specific numerical values in various
aspects of Judaism can be shown to highlight the world’s hidden unity.
The origins
A look at the origins of the world allows a deeper understanding of this
intrinsic unity of the world.
Before the Beginning there was only the single unity of Hashem.
In the Beginning Hashem created the world. This was achieved by separating the
original disorder into many pairs. Among those listed in the Torah are:
Light and darkness
Day and night
Land and Sea
Heavens and Earth
And, finally ….
after the Beginning, Hashem created and separated the last of his creations, the
pinnacle, Man and Woman, and instructed them to leave their parents and
cleave to each other and become a single flesh.2 In essence we are commanded
1. Rambam. Hilchot Yesodai Hatorah. Chapter 1
2. ‫ על כן יעזב איש את אביו ואת אמו ודבק באשתו והיו לבשר אחד‬:)‫כד‬:‫בראשית (ב‬
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We can use this command of uniting Man and Woman, as a ‫ בנין אב‬, a prototype,
of how we should relate to the other ‘separations’ that Hashem brought about.
Even though the world appears to be built of opposites, our aim is to find the
commonality between all the parts and, so to speak, be a partner with Hashem
to complete the creation by harmonizing these opposites.5
1,2 and 3
The famous Jewish philosopher and mystic, Rabbi Judah Loew, known also as
the Maharal of Prague (1525-1609)6 explains the spiritual significance of certain
numbers as they appear in Jewish law and legend. He explains that the number
1 is the ultimate symbol of unity. The number 2, as the first number after 1,
represents diversity – 2 opposites. This explanation blends with the concept
that the creation consisted of separating unified items into pairs of opposites
as listed above.
3. The uniting of the pieces is not exactly to the original state. The Gemara tells us that Man and
Woman were originally connected back-to-back, which was considered an incomplete unity, since
they could not interact with each other. The ideal unity is achieved by fulfilling the command and
uniting face-to-face.
4. See the midrash that states that there are 3 partners in creating the newborn: The father, the mother
and Hashem:
‫ אביו מזריע בו לובן שממנו‬,‫ תני בזמן שהולד נוצר במעי אמו שלשה הם שותפין בו הקבה ואביו ואמו‬:‫קהלת רבה פרשה ה‬
‫ אמו מזרעת אודם שממנו הדמים והעור והבשר ושער ושחור‬,‫הלובנים והמוח והצפרנים ולובן שבעין והעצמות והגידין‬
‫ והקב”ה יתברך שמו ויתרומם זכרו נותן בו עשרה דברים ואלו הן רוח ונשמה וקלסתר פנים ומראית עינים‬,‫שבעינים‬
.‫ושמיעת אזנים ודבור שפתים ונשיאות ידים והילוך רגלים וחכמה ובינה ועצה ודעת וגבורה‬
5. It is a fairly common theme amongst the commentators that Hashem created an incomplete world in
order for man to be a partner in the completion of creation. This is seen by the verse in Bereshit:
‫לקים לעשות‬-‫ “( אשר ברא א‬as Hashem created the world, to do”) where the word ‫“( לעשות‬to do”) is
explained as what Hashem wanted man to do. It is also one of the reasons given for circumcision,
where man is given the opportunity to change the natural state of his body, thereby becoming a
partner in completing the creation of man.
6. Netzach Yisrael Chapter 3.
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One an ODD Number
to undo the original separation between Man and Woman at the time of
creation and bring the pieces together again – but in a more organized form.3
By Man and Woman uniting, they are completing the process of creation. It
is interesting to note that in doing this they ‘create’ life, emulating Hashem’s
creation.4
He goes on to explain that the number 3 symbolizes the harmony that can
be found between the opposites that are represented by 2. Hence the two
opposites of creation, Man and Woman, combine and give birth to a single
child who has common features of the two parents.
All objects in our world are perceived as non-singularities. This unification
can provide an understanding of the original unity representing Hashem,
which otherwise is difficult to comprehend in our diverse world.
One an ODD Number
Generalizing the concept
In this example, the odd number (3) that followed the even number (2) provided
insight into the unity between the objects represented by the even number.
This idea that the odd number (n+1) which follows an even number (n) can provide an
understanding of the unified inter-relationship between the n objects represented by the
even number, can be generalized for other pairs of odd-even numbers
Several examples from Jewish sources, with an emphasis on the Calendar,
illustrate this.
The Festivals: one dimensional dualism
We normally think of there being three main pilgrimage festivals ( ‫)רגלים‬
mandated by the Torah. The Talmud states, however, that ‫– שמיני עצרת‬the eighth
day of Sukkot—is a festival (‫ )רגל‬in its own right7. There are, thus, six annual
holydays: the four pilgimage festivals along with Rosh Hashana and Yom
Kippur. These can be split into three pairs: Pesach – Shavuot; Sukkot - Shmini
Atzeret; Rosh Hashanah - Yom Kippur. The members of each of these pairs of
holy days are linked by a third period.
Pesach and Shavuot
Pesach represents the physical redemption from slavery. It is the start of
the Israelite nation, the time at which we were taken out of Egypt purely
7. Rosh Hashana 4b
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Sukkot and Shmini Atzeret
Sukkot represents the physical protection of the Jews in the desert. As with
Pesach, the emphasis is on the abundance received from Hashem, while
the recipients were passive. During the 40 years in the desert, the Israelites
were completely dependent on Hashem for their basic sustenance. On
Shmini Atzeret/ Simchat Torah, in contrast, we celebrate the relationship
between Hashem and his people, with emphasis on the recipients.8 Just
as in Pesach, Hashem redeemed us physically, so did He provide us
physical protection on Sukkot. Just as we received the Torah as a spiritual
complement on Shavuot, so do we celebrate with the Torah on Simchat
Torah. Similar to Pesach and Shavuot, these two festivals are linked by the
7 days of Sukkot.
Rosh Hashana and Yom Kippur
The two Yamim Noraim have a similar relationship between them. On
Rosh Hashana, we rely on Hashem to save the world and it is a holiday
8. See Rashi :(‫לה‬:‫)רשי במדבר כט‬
‫ אמר להם המקום בבקשה מכם עשו לי סעודה‬,‫ומדרשו באגדה לפי שכל ימות הרגל הקריבו כנגד שבעים אומות וכשבאין ללכת‬
‫קטנה כדי שאהנה מכם‬
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One an ODD Number
by Hashem’s involvement. The Israelites were almost entirely passive. The
physical redemption was only a stepping stone to the spiritual redemption,
symbolized by the receiving of the Torah on Mount Sinai on Shavuot.
Shavuot is the spiritual counterpart of Pesach. In contrast to the emphasis
on G-d’s role in the events leading to the Exodus, the focus on Shavuot is on
the nation as receivers of the influence and their ability to receive, nurture
and develop this influence as seen by their declaration of “We will obey
and listen” - “‫”נעשה ונשמע‬.
This pair of festivals is linked by another period of time - the 7
weeks of the Omer, each of the weeks also consisting of 7 days.
As will be shown in the section on Shabbat and Shmitta below,
the number 7 has a strong association with the unity of the world.
including the miztva to eat, drink and be happy9. On Yom Kippur, however,
the responsibility is on the recipients with the emphasis on prayer and
fasting and the activities in the temple. These two days are linked by the
intervening seven days of repentance.
Purim and Chanukka
One an ODD Number
The later rabbinically ordained holidays, Purim and Channuka, also
have some of the aspects of this duality. Purim emphasizes the physical
salvation from annihilation by Haman, with the celebrations including
physical acts like give gifts and charity, eating a meal and drinking wine.
On Chanukah, on the other hand, we recall a spiritual redemption where
the Jews managed to avoid idol worship. The mitzvah of lighting candles,
symbolizing spiritual light, is therefore more appropriate.
Yom Ha’atzma’ut and Yom Yerushalayim
Even the two holidays of contemporary origin seem to follow the same
duality. On Yom Ha’atzma’ut we celebrate the establishment of the State
of Israel, the state that allows us to protect ourselves against the physical
threat of annihilation. It took as long as 19 years later, on Yom Yerushalayim,
till we began to celebrate the spiritual counterpart with the unification of
the “body” of Israel, with its spiritual “heart”, Jerusalem.10 Both these
contemporary holidays fall within the 7 weeks of the Omer within the
similar Pesach-Shavuot pair.
Shabbat and Shmitta - 3 Dimensional duality
The Maharal11 explains that each of the 6 days of the week represents a different
extreme in each of the 3 dimensions or 6 directions (North, South, West, East,
Top and Bottom). Each of these opposites has its own unique characteristics (for
9. ‫ ואין מתענין ברה‬,‫ אוכלים ושותים ושמחים‬:‫שולחן ערוך אורח חיים סימן תקצז סעיף א‬
10. It’s interesting that the word ‫ ירושלים‬is composed of the words ‫יראו שלם‬, indicating that Jerusalem is a
completion of process which includes the whole.
11. Tiferet Yisrael. Chapter 2
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Combined with the 6 festivals (the 4 ‫ רגלים‬and 2 ‫)ימים נוראים‬, Shabbat can
also be viewed as a 7th component. While Shabbat is not a “Chag”, it is a
“Mo’ed” (Vayikra 32:2) like the other festivals. Appearing regularly every
week, independent of the date of the year (which is dependent on the New
Moon declared by the Bet Din) – Shabbat acts as a central point of unity
between the festivals.
In the same way that Shabbat unites the 6 dimensions on a personal level,
the Sabbatical year, Shmitta, fills the role of uniting the 6 dimensions on the
national level. During the Shmitta, all the fruit of the land are shared among all
the people and loans are annulled. In other words, the social differences that
tend to remove the commonality between people are temporarily canceled,
reminding everyone that the world and its inhabitants are all part of the same
great system. A similar effect is seen in the weekly Shabbat when refraining
from the work that socially differentiates people. On the Jubilee year, which
occurs every 50 years (after 7 Shmitta years – or 7 x 7 years, similar to the
12. The idea of Shabbat representing the wholeness of the world is seen in the word “‫ ”ויכולו‬translated
that G-d “completed” the creation of the world. The word “‫ ”ויכולו‬is derived from the Hebrew word
“‫ ”הכללה‬indicating completeness or wholeness.
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One an ODD Number
example, the sun rising in the East representing new beginnings and setting in
the West representing the completion of a cycle) which could lead one to the
erroneous conclusion that the world is controlled by many conflicting forces.
The Shabbat is the force in the middle that connects these 6 opposites together
into a single coordinated system. This is why the Shabbat is a “reminder of the
creation of the world” (‫)זכר למעשה בראשית‬. This reminder of the creation tells us
that the source of the multi-faceted world we live in is really one. The Shabbat
is therefore another example of the odd number (7) that follows the 6 days of
the week and of creation that shows the intrinsic unity of the other days.12
Since the 6 directions and days of the week are the basic components of the
world (representing the 3 spatial dimensions and the 4th dimension of time),
its unifying odd number, 7, is a strong symbol of unity. Seven is therefore the
number of days that combines the 4 festivals (‫)רגלים‬. As discussed above seven
weeks of seven days each link between Pesach and Shavuot, while the 7 days
of Sukkot link the first holyday of the festival and Shmini Atzeret.
One an ODD Number
counting of the Omer discussed above) the message is enhanced with the
freeing of slaves, he annulment of loans and the returning of land that may
have been sold due to financial difficulties.
It is interesting that the curses in the Torah are also listed at 7 groups of 7
curses. Just as the World is built and exists through the number 7, so it is
destroyed through 7 x 7 stages if its inhabitants do not fulfill the aim for
which it was created. Note that the term “‫( ”שבע על חטאתיכם‬meaning that we
will be punished seven-fold for our sins) appears 3 times in Vayikra 26 in
the description of the curses. The great commentator, Rashi (ibid), provides a
detailed listing of the 7 groups of 7 sins that resulted in these curses.
The Mishkan – Two dimensional duality
The Mishkan (Tabernacle or Mobile Temple in the desert contained 5 main
vessels:
1. The Holy Ark (‫ – )ארון קודש‬in the West
2. The Table with the Show-Bread (‫ – )שולחן עם לחם הפנים‬in the North
3. The Menorah– in the South
4. The small altar for incense (‫ )מזבח הקטרת‬- in the centre
5. The large altar for burning the sacrifices (‫ – )מזבח העולה‬in the East
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In the West, the Holy Ark is the holiest of all the vessels, housing the Ten
Commandments. It is located in the “Holy of Holies”, only seen for a few
minutes, on the holiest day of the year, Yom Kippur, by the holiest person,
the High Priest making it the symbol of holiness and modesty. In the East
is the large altar. Not only is it located on the side opposite to the Ark, but it
represents the opposing concepts to the Ark. Unlike the Ark, the large altar is
located in the open-air part of the Mishkan, allowing it to be seen even from
outside the Mishkan. Its purpose is to accept the physical offerings (animal
and wheat sacrifices).
A similar contrast is seen between the Menorah and the Table. The former
represents light, the sign of spirituality, while the latter represents physical
sustenance.15
Observation of the diametrically opposing vessels could lead to an erroneous
conclusion that the Mishkan is not one single integrated unit. The small altar
in the middle, the altar on which the incense is burnt, indicates that the whole
Mishkan, like the World it represents, is part of a single integrated system. The
sense of smell triggered by the incense is a combination of the physical and
spiritual, subtle yet consisting of physical particles. The word ‫( קטרת‬incense) is
based on the same root as ‫קטר‬, which mean to tie together in Aramaic.
Just as Shabbat ties together the 3 pairs of the days of the week, so the Small
Altar ties together the other 4 vessels in the Mishkan. To emphasize the point
13. Shmot: chapter 25
14. Shmot: chapter 30:1-10
15. ‫ שלחן בצפון ומנורה בדרום‬:‫ וסימניך‬,‫ יצפין‬- ‫ ושיעשיר‬,‫ ידרים‬- ‫ הרוצה שיחכים‬:‫ ב) אמר רבי יצחק‬:‫בבא בתרא (כה‬
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One an ODD Number
In the first description of the Mishkan13, the Torah describes the physical
building in great detail and describes 4 of the vessels, but not the small altar
of the incense. Only after several chapters14, including many other details of
the Mishkan and the Priestly Garments, does the Torah finally get to the small
altar. One explanation for this is that the small altar represents the central force
in the middle of the 4 extremes, similar to the Shabbat that links the 6 days of
the week, as described in the previous section.
that all the additional details of the tabernacle are also part of this single well
integrated system, the Torah postponed the description of the small altar until
after the list of all the other components of the tabernacle.
The Seder – 4 cups and 4 terms of redemption
One an ODD Number
Another familiar example of the numbers 4 and 5 can be seen in the four cups
of wine that we drink on the seder night. These cups recall the 4 terms of
redemption used in the bible:16
‫ ולקחתי‬,‫וגאלת‬, ‫והצלתי‬, ‫והוצאתי‬
“And I will take you out [of Egypt], and I will save you, and I will redeem you,
and I will take you [to Me]”
There is a 5th cup with a matching 5th term of redemption “‫”והבאתי‬. However
this cup is different from the other cups. It’s the cup of Eliyahu, which we don’t
drink but serve in honor of the prophet Eliyahu. Similar to the examples above,
we can see this cup as the middle point or the soul of the other cups, uniting
them into a single coordinated system which is appropriate for Eliyahu,
the prophet who will announce the final redemption and is the symbol
redemption.17
The 5th verse corresponding to this cup, deals with Hashem bringing the Jewish
People to the Land of Israel. The first 4 steps of redemption are preparation for
the ideal of the complete redemption when the people are living as a nation in
their own land. Again this 5th term of redemption is the central soul, uniting
the other terms or stages of redemptions to a single coordinated goal.
16. ‫שמות ו‬
‫(ו) לכן אמר לבני ישראל אני ה והוצאתי אתכם מתחת סבלת מצרים והצלתי אתכם מעבדתם וגאלתי אתכם בזרוע נטויה‬
:‫ובשפטים גדלים‬
:‫להיכם המוציא אתכם מתחת סבלות מצרים‬-‫להים וידעתם כי אני ה א‬-‫(ז) ולקחתי אתכם לי לעם והייתי לכם לא‬
:‫(ח) והבאתי אתכם אל הארץ אשר נשאתי את ידי לתת אתה לאברהם ליצחק וליעקב ונתתי אתה לכם מורשה אני ה‬
17. ‫מלאכי פרק ג‬
:‫(כג) הנה אנכי שלח לכם את אליה הנביא לפני בוא יום ה הגדול והנורא‬
:‫(כד) והשיב לב אבות על בנים ולב בנים על אבותם פן אבוא והכיתי את הארץ חרם‬
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The Jewish year is a combination of solar and lunar calendars. The month is
lunar, consisting of approximately 29.5 days. This results in a year of 354 days
(29.5 days x 12 months), approximately 11.25 days shorter than the solar year.
To keep the festivals, which are seasonal, synchronized with the lunar year,
the Jewish calendar adds a 13th month every 2 or 3 years (7 times over a 19
year cycle).
Similar to the way the Maharal sees the number 6 as representing the 6
directions or sides of the cube, he sees the number 12 also representing spatial
reality - there are 12 edges in the cube, shown by the lines in the diagram
below.18.
Following the principle of the sequential odd number, the number 13 indicates
that the 12 sides of spatial reality come from a single source. This would
explain the special nature of the 13th month, Adar Bet: the month that has the
ability of ‫ונהפוך הוא‬, the ability to turn an absolutely negative situation into an
extremely positive one, as shown in the story of Purim that occurs in Adar.19
The fact that the number 13 shows us that there is a unity in the world, causes
us to recognize that G-d is the single creator and in turn should influence us
to become better people. This would explain why the number 13 has a special
positive significance with the 13 attributes of Hashem, which are used as a
guaranteed means to forgive, redeem and save the nation.
18. The kabbalists also view the number 12 as representing the 6 dimensions viewed separately from
a positive and negative point of view
19. Interestingly the numerical value of the Hebrew work for one – ‫ – אחד‬is 13 (= 4+8+1)
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One an ODD Number
The months and the tribes: 12 Dimensions
One an ODD Number
In a similar fashion, although there are traditionally 12 tribes in the Nation
of Israel, there is a 13th tribe. Each tribe consists of the descendents of one
of Jacob’s sons. Before Jacob passes away (Bereshit 48:5)20, he blesses his son
Joseph by declaring that Joseph’s two sons were to become separate tribes.
This increases the number of tribes to 13. Later the tribe of Levi gains a special
priestly status, so that the number of ‘standard’ tribes is reduced back to 12.
So Levi, as the 13th tribe, is the central point, the link to spirituality that
emphasizes the message that each tribe with its special abilities and powers is
part of an inseparable nation, with all the tribes working together for a single
cause (for example Yissachar and Zevulun splitting the physical and spiritual
responsibilities between them). Levi is the tribe from which the Priests came.
Levi is also the tribe that was not assigned a section of the land, other than
the Levite towns, showing that as the 13th tribe they were relatively removed
from the physical land. This message is seen graphically when looking at the
way the camps of the tribes in the desert were organized. There was a camp in
each the four directions, with three tribes per camp. The tribe of Levi was in
the center next to the tabernacle.21
Conclusions
When Hashem created the world, He created a world in which the unity
and spirituality are hidden22. The examples listed above, show a consistent
message of the hidden unity in the world. This places a responsibility of the
people of the world in general, and specifically the Jewish Nation, to reveal this
unity and perform activities to strengthen the harmony in the world.
Using this view as a starting point, the Bible and our other sources and
commandments can be viewed with an enhanced understanding. This
article is intended to provide a perspective that can be used to understand
20. I heard this from Rav Shabtai Sabato
21. Bamidbar (Chapter 2)
22. The word for World – ‫ – עולם‬is based on the word – ‫ – נעלם‬meaning “hidden”. The word for
“Nature” – ‫ הטבע‬- - is based on the word meaning “submerged”. However the latter also has the
same numerical value as the one of Hashem’s name – ‫לקים‬-‫א‬. The Kabalists use this as a proof that
Godliness exists in nature in a hidden fashion. (‫ אור לוי – הרב לוי נחמני‬page 48)
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Yehuda Zaks made Aliyah from South Africa in 1983 after receiving a BSc in Electrical
Engineering at Wits University. After working 8 years in South Africa and Israel, he
joined NDS 16 years ago as a verifier programmer for the analog and D2MAC systems.
With the emergence of digital TV, he ported the DIRECTV verifier to the DVB standard,
including the original porting to the uCOS operating system. In 1995, Yehuda moved to
Project Management, delivering the Foxtel analog project in Australia and then led the
integration for the DVB STB for the DigiStar and SkyLA projects. This was followed by
7 years delivering and supporting the BSkyB Digital system including the delivery of
the first XTV and Interactive systems by NDS. When NEWS Corp acquired DIRECTV,
Yehuda was assigned VP of delivery, managing the introduction of CA, middleware, XTV
and interactive to DIRECTV. Currently Yehuda is responsible for the delivery of the VG
Express, Mobile and IPTV products and the customers in Israel, Korea and China.
Yehuda lives with his wife and 6 children in Bet El. He feels that the human interaction and
divrei torah (as symbolized by the Chidushei Torah books) are the “soul” of company that
provide a significant part of the motivation of the company’s technological success.
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One an ODD Number
the world and its Creator in an integrated fashion. Hopefully, through this
we can be partners in achieving the blessing the World received after the
creation: ‫א) ויכלו השמים והארץ וכל צבאם‬:‫ )בראשית ב‬- “The Heavens and the Earth
reached completion”